INVERSE FUNCTIONS

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

f^-1(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse reflect over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean for two functions to be inverses of each other?

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain, then f and g are inverses.

Tags

CCSS.HSF-BF.B.4B

Front

What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of an inverse function?

Back

The range of the inverse function is the domain of the original function.

Tags

CCSS.HSF-BF.B.4C

Front

If f(1) = 5, what is f^-1(5)?

Back

f^-1(5) = 1.

Tags

CCSS.HSF-BF.B.4C

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function's graph over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = x², is f^-1(x) a function?

Back

No, because f(x) = x² is not one-to-one; it fails the horizontal line test.